BSA, Norton and Triumph are the main three where parts are available quite easily from many classic parts dealers.
Choosing a model would be a little harder and depending on how fat your wallet is.
For example in the BSA range, the humble BSA Bantam would be a very easy project, loads of parts and would not cost a packet.
But if you decided to go to the other end of the range a Rocket 3, would cost a tidy sum of money to restore, and for a Gold Star you would most probably need very deep pockets.
It could be cheaper to buy a bike already restored.